Two weight inequalities for bilinear forms

• Autores: Kangwei Li
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 1, 2017, págs. 129-144
• Idioma: inglés
• DOI: 10.1007/s13348-016-0182-2
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let 1\le p_0 p,q q_0\le \infty . Given a pair of weights (w,\sigma ) and a sparse family {\mathcal {S}}, we study the two weight inequality for the following bi-sublinear form \begin{aligned} B(f, g)= \sum _{Q\in {\mathcal {S}}}\langle |f|^{p_0}\rangle _Q^{\frac{1}{p_0}} \langle |g|^{q_0'}\rangle _Q^{\frac{1}{q_0'}}\lambda _Q\le \mathcal N\Vert f\Vert _{L^{p}(w)}\Vert g\Vert _{L^{q'}(\sigma )}. \end{aligned} When \lambda _Q=|Q| and p=q , Bernicot, Frey and Petermichl showed that B(f, g) dominates \langle Tf, g\rangle for a large class of singular non-kernel operators. We give a characterization for the above inequality and then obtain the mixed A_p-A_\infty estimates and the corresponding entropy bounds when \lambda _Q=|Q| and p=q . We also propose a new conjecture which implies both the one supremum conjecture and the separated bump conjecture.

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